All-sky search for gravitational-wave
bursts in the second joint LIGO-Virgo run
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Citation
Abadie, J. et al. “All-sky Search for Gravitational-wave Bursts in
the Second Joint LIGO-Virgo Run.” Physical Review D 85.12 (2012):
122007. © 2012 American Physical Society.
As Published
http://dx.doi.org/10.1103/PhysRevD.85.122007
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American Physical Society
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Final published version
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http://hdl.handle.net/1721.1/72147
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All-sky search for gravitational-wave bursts in the second joint LIGO-Virgo run
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M. E. Zucker,20,zand J. Zweizig1,z (*The LIGO Scientific Collaboration)
(†The Virgo Collaboration)
1LIGO - California Institute of Technology, Pasadena, California 91125, USA 2California State University Fullerton, Fullerton California 92831 USA
3SUPA, University of Glasgow, Glasgow, G12 8QQ, United Kingdom
4Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universite´ de Savoie,
CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
5aINFN, Sezione di Napoli, I-84084 Salerno, Italy
5bUniversita` di Napoli ’Federico II’, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, I-84084 Salerno, Italy 5cUniversita` di Salerno, Fisciano, I-84084 Salerno, Italy
6LIGO - Livingston Observatory, Livingston, Louisiana 70754, USA
7Albert-Einstein-Institut, Max-Planck-Institut fu¨r Gravitationsphysik, D-30167 Hannover, Germany 8Leibniz Universita¨t Hannover, D-30167 Hannover, Germany
9aNikhef, Science Park, Amsterdam, the Netherlands, 1081 HV Amsterdam, the Netherlands 9bVU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, the Netherlands
10National Astronomical Observatory of Japan, Tokyo 181-8588, Japan 11University of Wisconsin–Milwaukee, Milwaukee, Wisconsin 53201, USA
12
University of Florida, Gainesville, Florida 32611, USA
13University of Birmingham, Birmingham, B15 2TT, United Kingdom 14aINFN, Sezione di Roma, I-00185 Roma, Italy
14bUniversita` ’La Sapienza’, I-00185 Roma, Italy
15LIGO - Hanford Observatory, Richland, Washington 99352, USA
16Albert-Einstein-Institut, Max-Planck-Institut fu¨r Gravitationsphysik, D-14476 Golm, Germany 17Montana State University, Bozeman, Montana 59717, USA
18European Gravitational Observatory (EGO), I-56021 Cascina (PI), Italy 19Syracuse University, Syracuse, New York 13244, USA
20LIGO - Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
21APC, AstroParticule et Cosmologie, Universite´ Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris,
Sorbonne Paris Cite´, 10, rue Alice Domon et Le´onie Duquet, 75205 Paris Cedex 13, France
22Columbia University, New York, New York 10027, USA 23aINFN, Sezione di Pisa, I-53100 Siena, Italy 23bUniversita` di Pisa; I-56127 Pisa, I-53100 Siena, Italy
23cUniversita` di Siena, I-53100 Siena, Italy 24
Stanford University, Stanford, California 94305, USA
25aIM-PAN 00-956 Warsaw, Poland
25bAstronomical Observatory Warsaw University, 00-478 Warsaw, Poland 25cCAMK-PAN, 00-716 Warsaw, Poland
25dBiałystok University, 15-424 Białystok, Poland 25eNCBJ, 05-400 S´wierk-Otwock, Poland 25fInstitute of Astronomy, 65-265 Zielona Go´ra, Poland
26The University of Texas at Brownsville and Texas Southmost College, Brownsville, Texas 78520, USA 27San Jose State University, San Jose, California 95192, USA
28
Moscow State University, Moscow, 119992, Russia
29aLAL, Universite´ Paris-Sud, IN2P3/CNRS, F-91898 Orsay, France 29bESPCI, CNRS, F-75005 Paris, France
31University of Western Australia, Crawley, WA 6009, Australia 32The Pennsylvania State University, University Park, Pennsylvania 16802, USA
33aUniversite´ Nice-Sophia-Antipolis, CNRS, Observatoire de la Coˆte d’Azur, F-06304 Nice, France 33bInstitut de Physique de Rennes, CNRS, Universite´ de Rennes 1, 35042 Rennes, France 34Laboratoire des Mate´riaux Avance´s (LMA), IN2P3/CNRS, F-69622 Villeurbanne, Lyon, France
35Washington State University, Pullman, Washington 99164, USA 36aINFN, Sezione di Perugia, I-06123 Perugia, Italy
36bUniversita` di Perugia, I-06123 Perugia, Italy 37a
INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Italy
37bUniversita` degli Studi di Urbino ’Carlo Bo’, I-61029 Urbino, Italy 38University of Oregon, Eugene, Oregon 97403, USA
39Laboratoire Kastler Brossel, ENS, CNRS, UPMC, Universite´ Pierre et Marie Curie, 4 Place Jussieu, F-75005 Paris, France 40University of Maryland, College Park, Maryland 20742 USA
41Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain 42University of Massachusetts - Amherst, Amherst, Massachusetts 01003, USA
43Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario, M5S 3H8, Canada 44Tsinghua University, Beijing 100084 China
45University of Michigan, Ann Arbor, Michigan 48109, USA 46Louisiana State University, Baton Rouge, Louisiana 70803, USA 47The University of Mississippi, University, Mississippi 38677, USA
48Charles Sturt University, Wagga Wagga, NSW 2678, Australia 49Caltech-CaRT, Pasadena, California 91125, USA 50INFN, Sezione di Genova, I-16146 Genova, Italy 51Pusan National University, Busan 609-735, Korea 52
Australian National University, Canberra, ACT 0200, Australia
53Carleton College, Northfield, Minnesota 55057, USA 54The University of Melbourne, Parkville, VIC 3010, Australia
55Cardiff University, Cardiff, CF24 3AA, United Kingdom 56aINFN, Sezione di Roma Tor Vergata, Italy 56bUniversita` di Roma Tor Vergata, I-00133 Roma, Italy
56cUniversita` dell’Aquila, I-67100 L’Aquila, Italy
57University of Salerno, I-84084 Fisciano (Salerno), Italy and INFN (Sezione di Napoli), Italy 58The University of Sheffield, Sheffield S10 2TN, United Kingdom
59WIGNER RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklo´s u´t 29-33, Hungary 60aINFN, Gruppo Collegato di Trento, I-38050 Povo, Trento, Italy
60bUniversita` di Trento, I-38050 Povo, Trento, Italy 60cINFN, Sezione di Padova, I-35131 Padova, Italy 60dUniversita` di Padova, I-35131 Padova, Italy
61Inter-University Centre for Astronomy and Astrophysics, Pune - 411007, India 62California Institute of Technology, Pasadena, California 91125, USA
63Northwestern University, Evanston, Illinois 60208, USA 64University of Cambridge, Cambridge, CB2 1TN, United Kingdom
65The University of Texas at Austin, Austin, Texas 78712, USA 66Rochester Institute of Technology, Rochester, New York 14623, USA
67Eo¨tvo¨s Lora´nd University, Budapest, 1117 Hungary 68University of Szeged, 6720 Szeged, Do´m te´r 9, Hungary
69Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX United Kingdom 70
Embry-Riddle Aeronautical University, Prescott, Arizona 86301 USA
71National Institute for Mathematical Sciences, Daejeon 305-390, Korea 72Perimeter Institute for Theoretical Physics, Ontario, N2L 2Y5, Canada 73University of New Hampshire, Durham, New Hampshire 03824, USA
74University of Adelaide, Adelaide, SA 5005, Australia 75University of Southampton, Southampton, SO17 1BJ, United Kingdom
76University of Minnesota, Minneapolis, Minnesota 55455, USA
77Korea Institute of Science and Technology Information, Daejeon 305-806, Korea 78Hobart and William Smith Colleges, Geneva, New York 14456, USA
79
Institute of Applied Physics, Nizhny Novgorod, 603950, Russia
80Lund Observatory, Box 43, SE-221 00, Lund, Sweden 81Hanyang University, Seoul 133-791, Korea 82Seoul National University, Seoul 151-742, Korea 83University of Strathclyde, Glasgow, G1 1XQ, United Kingdom
84Southern University and A&M College, Baton Rouge, Louisiana 70813, USA 85University of Rochester, Rochester, New York 14627, USA
86University of Sannio at Benevento, I-82100 Benevento, Italy and INFN (Sezione di Napoli), Italy 87Louisiana Tech University, Ruston, Louisiana 71272, USA
88McNeese State University, Lake Charles, Louisiana 70609 USA 89Andrews University, Berrien Springs, Michigan 49104 USA
90Trinity University, San Antonio, Texas 78212, USA
91Southeastern Louisiana University, Hammond, Louisiana 70402, USA
(Received 5 March 2012; published 20 June 2012)
We present results from a search for gravitational-wave bursts in the data collected by the LIGO and Virgo detectors between July 7, 2009 and October 20, 2010: data are analyzed when at least two of the three LIGO-Virgo detectors are in coincident operation, with a total observation time of 207 days. The analysis searches for transients of duration& 1 s over the frequency band 64–5000 Hz, without other assumptions on the signal waveform, polarization, direction or occurrence time. All identified events are consistent with the expected accidental background. We set frequentist upper limits on the rate of gravitational-wave bursts by combining this search with the previous LIGO-Virgo search on the data collected between November 2005 and October 2007. The upper limit on the rate of strong gravitational-wave bursts at the Earth is 1.3 events per year at 90% confidence. We also present upper limits on source rate density per year and Mpc3 for sample populations of
standard-candle sources. As in the previous joint run, typical sensitivities of the search in terms of the root-sum-squared strain amplitude for these waveforms lie in the range 5 1022 Hz1=2 to 1 1020 Hz1=2. The combination of the two joint runs entails the most sensitive all-sky search
for generic gravitational-wave bursts and synthesizes the results achieved by the initial generation of interferometric detectors.
DOI:10.1103/PhysRevD.85.122007 PACS numbers: 95.85.Sz, 04.80.Nn, 07.05.Kf, 95.30.Sf
I. INTRODUCTION
Astrophysical sources of transient gravitational waves (duration of & 1 s) [1] include merging compact binary systems consisting of black holes and/or neutron stars [2,3], core-collapse supernovae [4], neutron star collapse to black holes [5], star-quakes associated with magnetar flares [6] or pulsar glitches [7], cosmic string cusps [8], and other violent events in the Universe. Since many classes of gravitational-wave (GW) bursts cannot be modeled well—if at all—a search for those sources must be sensitive to the widest possible variety of waveforms.
This paper reports on a search for GW bursts occur-ring duoccur-ring the second joint observation run of the LIGO [9] and Virgo [10] detectors, which took place in 2009– 2010. This search makes no prior assumptions on source sky location, signal arrival time, or the waveform itself. Event rate upper limits from long-term searches of this category have been derived with networks of resonant bar detectors with spectral sensitivity limited to around 900 Hz in 1997–2000 [11,12] and in 2005–2007 [13,14]. Networks of interferometric detectors set more stringent upper limits for GW bursts on a wider bandwidth using the LIGO detectors in 2005–2006 [15–17] and during the first joint observation of LIGO and Virgo detectors in 2007 [18].
This second joint LIGO-Virgo search for GW bursts analyzed the frequency band spanning 64–5000 Hz. We
achieved a frequency-dependent sensitivity comparable to or better than that of the first joint run, and accumu-lated 207 days of observation time interlaced with periods of installing or commissioning major hardware upgrades. Moreover, for the first time a low-latency analysis was run with the goal of providing triggers for electromagnetic follow-ups of candidates by robotic op-tical telescopes [19], radio telescopes, and the Swift satellite [20,21]. In this paper we focus on the final results of the GW stand-alone search, which found no evidence for GW bursts.
This paper is organized as follows. In Sec.IIwe describe the second joint scientific run: we report on the LIGO and Virgo instrumental upgrades with respect to the first run and on data quality studies. In Sec. III we give a brief overview of the search: the search algorithm, background estimation, the simulations and the calibration uncertain-ties. The signal models (GW waveforms and source pop-ulations) we tested are described in Sec.III C. The results of the search are presented in Sec. IV, and astrophysical implications are discussed in Sec. V. The Appendices provide additional details on data characterization and analysis methods.
II. SECOND LIGO-VIRGO SCIENCE RUN The network of detectors used in this search comprises the two LIGO 4 km interferometers, denoted ‘‘H1’’ (located in Hanford, WA) and ‘‘L1’’ (Livingston, LA), as
well as the Virgo 3 km interferometer, denoted ‘‘V1’’ (close to Pisa, Italy).1
The LIGO detectors operated from July 7, 2009 to October 20, 2010 in their sixth science run (S6). The Virgo detector operated from July 7, 2009 to January 8, 2010 in its second science run (VSR2) and again from August 11 to October 20, 2010 in its third science run (VSR3).
As in the first joint LIGO-Virgo run [18,22], the opera-tion of three differently oriented and widely separated detectors allows for reasonably complete coverage of the sky for at least one gravitational-wave polarization com-ponent as well as the recovery of some source character-istics such as sky location [19,23,24].
A. Detector upgrades
Before the beginning of the runs, several detector hard-ware upgrades were implemented in order to prototype new subsystems planned for the next generation of detec-tors, referred to as ‘‘advanced detectors’’ [25,26], expected to start observations in 2015. The upgrades of the LIGO detectors for S6 include a higher power 35 W laser, the implementation of a DC readout system, a new output mode cleaner, and an advanced LIGO seismic isolation table [27]. The upgrades of the Virgo detectors were achieved in two steps. For VSR2, Virgo operated with a more powerful laser and a thermal compensation system. Virgo then went offline to install new test masses consist-ing of mirrors hung from fused silica fibers [28]. Virgo resumed observations in August 2010 with VSR3. Best sensitivities, in terms of noise spectral densities, of the LIGO and Virgo detectors achieved during their second joint run (henceforth defined as S6-VSR2/3), as a function of signal frequency, are shown in Fig.1.
B. Data quality
To mitigate the consequences of new hardware installa-tions and detector commissioning during this run, signifi-cant effort has been made to identify and characterize instrumental or data acquisition artifacts, periods of de-graded sensitivity, or an excessive rate of transient noise due to environmental conditions [29]. During such times, the data were tagged with data quality flags (DQFs). Following the same approach used in previous searches [16–18], these DQFs are divided into three categories depending on their impact on the search and on the under-standing of the behavior of the detector. A further descrip-tion of DQF categories is presented in AppendixA.
After DQFs have been applied, the total analyzable time for the S6-VSR2/3 run is 242.8 days for H1, 220.2 days for L1, and 187.8 days for V1.
III. SEARCH OVERVIEW
In this analysis, we considered all four available detector network configurations: the three detector network, H1L1V1, and the three combinations of detector pairs, H1L1, H1V1 and L1V1. We decided a priori to search for GW bursts in the entire available time of threefold observation and in the remaining exclusive times of the twofold networks. Table I reports the total (nonoverlap-ping) coincident observation time for each configuration of detectors searched for GW signals. Information about dis-tinct subperiods of the run may be found in AppendixC.
Because of the commissioning breaks and installation activities described in Sec.II, the total observation time is dominated by twofold configurations.
The useful frequency band is limited to 64–5000 Hz by the sensitivity of the detectors and by the valid range of data calibration. For computational reasons, the event search was performed separately in two suitable bands, 64–2048 Hz and 1600–5000 Hz, overlapping to preserve sensitivity to events with spectral power at intermediate frequencies. The analysis of the events (including the tun-ing of the search) was performed independently on each configuration of detectors and on three sub-bands, namely, 64–200 Hz, 200–1600 Hz and 1600–5000 Hz, by classify-ing the found events accordclassify-ing to their reconstructed cen-tral frequency. The motivation for this band splitting is to
FIG. 1. Noise spectra for the three LSC-Virgo detectors achieved during S6-VSR2/3.
TABLE I. Mutually exclusive observation time for each detec-tor configuration after the application of category 2 DQFs (see Appendix A for the definition of data quality flags and their categories).
Network H1L1V1 H1L1 L1V1 H1V1 Total Observation time [days] 52.2 84.5 28.9 41.0 206.6
1The 2 km detector at the Hanford site (H2) was
decommis-sioned before the second joint LIGO-Virgo run. During previous runs, the latter detector was mainly used to enforce additional event selection criteria by taking advantage of the special rela-tionship for GW signals from the co-located interferometers H1 and H2.
tune the search within event sets of homogeneous glitch behavior.
A. Search algorithm
This search is based on the coherent WaveBurst (cWB) algorithm [29], which has been used since LIGO’s fourth science run in various searches for transient GWs [16–18,30].
The cWB analysis is performed in several steps. First, detector data is decomposed into a time-frequency repre-sentation and then whitened and conditioned to remove narrow-band noise features. Events are identified by clus-tering time-frequency pixels with significant energy which is coherent among detectors and characterized using test statistics derived from the likelihood (which is also a measure of the signal energy detected in the network and is calculated as described in [16]). The primary statistics are the network correlation coefficient cc, which is a measure of the degree of correlation between the detectors, and the coherent network amplitude , which is propor-tional to the signal-to-noise ratio and is used to rank events within a homogeneous subperiod.
Both of these statistics are described in detail in [16]. The application of the event selection criteria is thoroughly described in [18,31].
Any gravitational-wave candidate event detected by cWB is subject to additional data-quality vetoes based on statistical correlations between the GW data channel and environmental and instrumental auxiliary channels; a sig-nificant correlation indicates the event may have been produced by local noise. Further details can be found in AppendixB.
B. Background estimation and search tuning A sample of ‘‘off-source’’ (background) events is re-quired to determine the selection thresholds to reject noise-induced events contaminating the ‘‘on-source’’ (fore-ground) measurement. We estimate the distribution of background events by performing the analysis on time-shifted data, typically in1 s steps. The shifts minimize the chance of drawing an actual GW into the background sample. To accumulate a sufficient sampling, this shifting procedure is performed hundreds or thousands of times without repeating the same relative time shifts among detectors. Background events corresponding to times which are flagged by data quality studies are discarded, just as an event candidate from the foreground would be.
Because of the different characteristics of the back-ground noise for the various subperiods between commis-sioning breaks and for the different frequency bands and networks, the thresholds on cc and are tuned separately for each homogeneous subperiod. Moreover, we consider the action of conditional DQFs (Category 3 DQFs, see Appendix A) on the event significance, by introducing a new ranking scheme which assigns lower significance to
events flagged by such DQFs. More details on this proce-dure are reported in AppendixD.
The thresholds reported in Table VII in AppendixDare selected to require a false alarm rate (FAR)& 1=ð8 yrÞ per frequency band. This choice for the FAR threshold corre-sponds to an overall false alarm probability (FAP) of 15% when considering the union of all searches per-formed (network configurations, subperiods, and fre-quency bands). ‘‘On-source’’ events at higher FAR
TABLE II. Values of h50%
rss and h90%rss (for 50% and 90%
detec-tion efficiency at the chosen thresholds of 1=ð8 yrÞ per frequency band), in units of 1022 Hz1=2, for linear and elliptical sine-Gaussian waveforms with the central frequency f0 and quality
factor Q. The center two columns are the h50%
rss for linear and
elliptical waveforms during the total S6 period measured for the H1L1V1 network. The rightmost columns report the values of h50%
rss and h90%rss over the whole S6-VSR2/3 for the combined
results (i.e. averaged over time) from all the networks. H1L1V1 All networks f0 Linear Elliptical Linear Elliptical
[Hz] Q h50% rss h50%rss h50%rss h90%rss h50%rss h90%rss 70 3 18.9 18.0 28.4 311.9 23.2 92.7 70 9 21.5 20.4 31.6 269.4 25.8 91.7 70 100 24.2 21.4 34.4 484.9 27.4 131.9 100 9 10.5 9.6 15.6 156.6 12.6 57.6 153 9 6.7 5.8 10.3 105.4 8.0 35.2 235 3 5.7 5.5 8.5 45.3 7.4 24.4 235 9 5.2 4.9 7.7 39.7 6.6 20.7 235 100 4.6 4.4 7.2 37.6 6.0 19.0 361 9 8.6 8.7 12.4 67.8 11.1 32.7 554 9 8.9 8.4 13.1 69.4 11.1 35.2 849 3 15.1 14.4 20.8 128.7 18.4 56.6 849 9 14.1 13.3 19.7 116.0 17.2 52.0 849 100 12.3 11.4 17.4 88.7 14.8 44.9 1053 9 16.9 17.5 24.2 133.5 21.9 63.9 1304 9 21.1 19.7 30.4 177.9 25.3 78.6 1615 3 41.6 54.5 349.8 1615 9 35.2 46.3 259.9 1615 100 28.3 38.8 219.3 1797 9 26.8 35.4 206.0 2000 3 41.6 51.8 322.9 2000 9 30.8 38.7 229.1 2000 100 27.4 36.0 181.8 2226 9 36.6 47.2 272.1 2477 3 51.6 61.2 425.9 2477 9 44.3 55.2 307.3 2477 100 34.6 46.3 233.5 2756 9 44.2 56.8 389.8 3067 3 74.1 81.7 600.0 3067 9 64.6 78.0 499.6 3067 100 41.1 53.8 278.2 3413 9 65.7 80.0 510.4 3799 9 81.7 99.3 719.9
are discarded as nonsignificant. Any ‘‘on-source’’ events passing the FAR threshold are instead selected for further follows-up investigations. Namely, we check for any addi-tional evidence about their origin and refine the measure-ment of their statistical significance (i.e. by performing additional independent time-shifted analyses to increase the statistics of the background estimates). This FAR threshold sets the overall sensitivity of the search.
C. Simulated signals and detection efficiencies In order to test the sensitivity of our search to gravitational-wave bursts, we add (‘‘inject’’) various ad-hoc software signals, both polarized and unpolarized, to the detector data and measure the detection efficiencies of the search. The injected waveforms can be parametrized as:
hþðtÞ hðtÞ ¼ A 1þ 2 2 " # HþðtÞ HðtÞ ; (3.1)
where A is the amplitude, the ellipticity2and Hþ=are
the waveforms for the two independent polarizations. In this search, we investigated elliptically polarized signals (i.e. uniformly chosen in [0, 1]), as well as sets of only linearly or circularly polarized waves ( fixed to 0 or 1, respectively). A variety of GW signal morphologies span-ning a wide range of signal durations, frequencies and amplitudes were tested. See Fig.2for a sample of repre-sentative waveforms from various families and TablesII, III, andIVfor the chosen waveform parameters.
The injected waveform families include: (i) Sine-Gaussian:
HþðtÞ ¼ expðt2=2Þ sinð2f0tÞ (3.2)
HðtÞ ¼ expðt2=2Þ cosð2f0tÞ; (3.3)
where ¼ Q=ðpffiffiffi2f0Þ. We consider waveforms of
this type with central frequencies f0chosen between
70 to 5000 Hz and quality factors Q ¼ 3, 9, 100. Sine-Gaussian waveforms with a few cycles are qualitatively similar to signals produced by the mergers of two black holes [2].
(ii) Gaussian:
HþðtÞ ¼ expðt2=2Þ (3.4)
HðtÞ ¼ 0; (3.5)
where the duration parameter is chosen to be one of 0.1, 1.0, 2.5, or 4.0 ms.
(iii) Ring-down waveforms:
HþðtÞ ¼ expðt=Þ sinð2f0tÞ (3.6)
HðtÞ ¼ expðt=Þ cosð2f0tÞ: (3.7)
We use several central frequencies from 1590 Hz to 3067 Hz, and decay times ¼ 0:2 s or Q ¼ 9. Ring-downs can occur in the end stages of black hole binary mergers. Longer duration ring-downs are also similar to signals predicted from the exci-tation of fundamental modes in neutron stars [32]. (iv) Band-limited white noise signals: The polarization components are bursts of uncorrelated band-limited white noise, time shaped with a Gaussian profile; Hþ and H have—on average—equal root mean
square amplitudes and symmetric shape about the central frequency (see Fig.2).
(v) Neutron star collapse waveforms: For a comparison with previous searches [17,18], we considered nu-merical simulations by Baiotti et al. [5], who mod-eled neutron star gravitational collapse to a black
FIG. 2. Representative waveforms injected into data for simulation studies. The top row is the time domain and the bottom row is a time-frequency domain representation of the waveform. From left to right: a 361 Hz Q ¼ 9 sine-Gaussian, a ¼ 4:0 ms Gaussian waveform, a white noise burst with a bandwidth of 1000–2000 Hz and characteristic duration of ¼ 20 ms and, finally, a ring-down waveform with a frequency of 2000 Hz and ¼ 1 ms.
2For binary sources, the ellipticity is the cosine of the source
inclination angle, i.e. the angle between the source rotational axis and the line of sight to Earth.
hole and the subsequent ring-down. As in previous searches, we chose the models D1 (a nearly spheri-cal 1:67Mneutron star) and D4 (a 1:86Mneutron
star that is maximally deformed at the time of its collapse into a black hole) to represent the extremes of the parameter space in mass and spin considered in the aforementioned work. Both waveforms are linearly polarized (H¼ 0) and their emission is
peaked at a few kHz.
The simulated signals were injected with many ampli-tude scale factors to trace out the detection efficiency as a function of signal strength. The amplitude of the signal is expressed in terms of the root-sum-square strain amplitude (hrss) arriving at the Earth, defined as
hrss ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z jhþðtÞj2þ jhðtÞj2dt s : (3.8)
The signal amplitude at a detector is modulated by the detector antenna pattern functions, expressed as follows:
hdetðtÞ ¼ Fþð; ;cÞhþðtÞ þ Fð; ;cÞhðtÞ; (3.9)
where Fþand Fare the antenna pattern functions, which
depend on the orientation of the wave front relative to the detector, denoted here in terms of the sky position (, ), and on the polarization angle c. The sky positions of simulated signals are distributed isotropically and polar-ization angles are chosen to be uniformly distributed.
The detection efficiency is defined as the fraction of signals successfully recovered using the same selection thresholds and DQFs as in the actual search. The detection efficiency of the search depends on the network
FIG. 3. Detection efficiency for selected waveforms as a func-tion of signal amplitude hrss for the H1L1V1 network. Top:
Comparison of detection efficiency for linear (L) and elliptical (E) sine-Gaussians with central frequencies of 235 and 1304 Hz. Middle: Comparison of detection efficiency for linear (L) and circular (C) ring-down signals with frequencies of 2090 and 2590 Hz. Bottom: Detection efficiency for white noise bursts with frequency spanning between 100 and 4500 Hz.
FIG. 4. Efficiency for the H1L1V1 network as a function of distance for the D1 and D4 waveforms predicted by polytropic general-relativistic models of neutron star collapse.
TABLE III. Values of h50%
rss and h90%rss (for 50% and 90%
detection efficiency at the chosen thresholds of 1=ð8 yrÞ per frequency band), in units of 1022Hz1=2, for linearly and circularly polarized ring-downs characterized by parameters f and . All networks f Linear Circular [Hz] [ms] h50% rss h90%rss h50%rss h90%rss 2000 1.0 47.3 288 34.8 78.9 2090 200 42.9 218 31.7 66.0 2590 200 52.2 255 39.1 79.5 3067 0.65 91.9 546 72.9 569
configuration and the selection cuts used in the analysis. Detection efficiencies for the H1L1V1 network for se-lected waveforms as a function of signal amplitude hrss
and as a function of distance (for the D1 and D4 waveforms from Baiotti et al. [5]) are reported in Figs. 3 and 4, respectively. As in the previous joint run, typical sensitiv-ities for this network in terms of hrss for the selected
waveforms lie in the range 5 1022 Hz1=2 to 1 1020 Hz1=2; typical distances at 50% detection
efficiency for neutron star collapse waveforms lie in the range50 pc to 200 pc.
Two convenient characterizations of the sensitivity, the hrss at 50% and 90% detection efficiency (h50%rss and h90%rss
respectively) are obtained from fitting the efficiency curves and are reported in TablesII, III, and IV for the various families. Notice that the threefold network, H1L1V1, has a better sensitivity than the weighted average over all net-works: twofold networks have3=4 of the analyzed live time, but feature a lower sensitivity.
D. Systematic uncertainties
The most relevant systematic uncertainty in the astro-physical interpretation of our results is due to the calibra-tion error on the strain data produced by each detector [33,34]. The effect of calibration systematics on network detection efficiency has been estimated by dedicated simu-lations of GW signals in which the signal amplitude and phase at each detector is randomly jittered according to the modeled distribution of calibration errors for that detector. The resulting network detection efficiency marginalizes the effect of the systematic uncertainties over the observa-tion time. The main effect can be parametrized as an overall shift of the detection efficiency curves along the signal strength axis. The largest effect over the injected signal waveforms was a 8% increase of the hrss amplitude
at fixed detection efficiency.3To produce the astrophysical limits shown in Sec. IV, we use the reduced detection efficiency curves obtained by shifting the original fits from Sec. III Cand the results in Tables II,III, andIV to 8% larger hrssvalues.
IV. SEARCH RESULTS
The on-source data have been analyzed following the procedures tuned through the investigation of the off-source background sample, as described in Appendix D. No on-source event has been found above the threshold false alarm rate of once in 8 years per frequency band, and the distribution of on-source events is in agreement with the measured background. Table V lists the five most significant on-source events, as ranked by their inverse false alarm rate (IFAR¼ 1=FAR), and taking into account the trial factor due to the three independent searches per-formed on the disjoint frequency bands.
In addition to the events reported in Table V, this search also detected an on-source event showing a chirp-ing waveform compatible with a compact binary coales-cence at a signal-to-noise ratio 17 in the H1L1V1 network. This event was first identified by a low-latency burst search within minutes of its occurrence on September 16, 2010 and was thoroughly investigated in follow-up studies. Its Inverse False Alarm Rate was estimated at 1.1 yr from comparison with the burst reference background over all trials. After the comple-tion of the analysis, this event was revealed to be a blind hardware injection [35] intended as an end-to-end test of the search for transient signals.4 As such, the event was removed from the final results.
Upper limits
The new null result can be combined with the previous ones from the latest scientific runs by LIGO and Virgo [16–18] to complete the results achieved by initial genera-tion interferometric detectors.
Assuming a Poisson distribution of astrophysical sources and in the special case of no surviving candidate
TABLE IV. Values of h50%
rss and h90%rss (for 50% and 90%
detection efficiency at the chosen thresholds of 1=ð8 yrÞ per frequency band), in units of 1022 Hz1=2, for band-limited white noise waveforms characterized by parameters flow, f,
and .
flow f H1L1V1 All networks
[Hz] [Hz] [ms] h50% rss h50%rss h90%rss 100 100 100 8.1 11.5 91.2 250 100 100 7.5 10.5 43.1 1000 10 100 15.5 22.5 93.6 1000 1000 10 30.5 39.7 130 1000 1000 100 76.8 76.7 492 2000 100 100 35.7 40.3 193 2000 1000 10 55.6 63.1 211 3500 100 100 71.8 90.3 332 3500 1000 10 114 125 371 3
Note that, due to an incomplete knowledge of the actuation resonances in [3000, 4000] Hz band of the Hanford detector, very conservative assumptions have been made on calibration uncertainties; the networks including H1 in that frequency band feature a large efficiency loss due to calibration systematics of 24%.
4Signal injections were performed via direct excitation of the
interferometer mirror test masses. Some of these hardware injections were intended to mimic a coherent GW excitation across the network and to provide an end-to-end verification of the detector instrumentation, the data acquisition system and the data analysis software. In addition to those, a blind injection challenge was realized consisting of injecting a few simulated signals at times not announced to the collaborations. This was done for the purpose of testing the data analysis pipelines and event validation protocols.
events, the 90% confidence upper limit is computed as in [36]: R90%¼ 2:3 P kkTk ; (4.1)
where 2:3 ¼ logð1–0:9Þ, kand Tkare, respectively, the
detection efficiency (calculated with selection thresholds as in Sec.III B) and the observation time of the network configuration k, including all available LIGO and LIGO– Virgo observations since November 2005 [16–18].
Figure 5 shows the upper limits on the rate of gravitational-wave bursts at the Earth as a function of signal strength (hrss) for selected sine-Gaussian
wave-forms. The second joint LIGO–Virgo run increases the previous total observation time by roughly 50%, totaling 1.74 yr. Therefore, the resulting 90% upper limit on the rate for strong signals (asymptotic behavior for k ! 100%)
decreases from 2.0 to 1:3 yr1 for the 64–1600 Hz band (from 2.2 to 1:4 yr1for the band above 1.6 kHz).
The results can also be interpreted as limits on the rate density of GW bursts (number per year and per Mpc3) assuming a standard-candle source, isotropically
distrib-uted, as previously reported in [18]. Denoting by h2 0 the
average value of the GW squared amplitude h2 rss at a
fiducial distance r0 from the source, the energy converted
to GWs is EGW¼ 2c3 G r 2 0f20h20; (4.2)
where f0is the central frequency of GW emission.
Considering a population of standard-candle sources randomly oriented with respect to the Earth and at a distance r0, we can interpret the h20 as the average GW
squared amplitude impinging on the Earth (e.g. averaged over source parameters such as inclination angle).
Equation (4.2) can then be used to estimate
h0ðEGW; f0; r0Þ and, in particular, sets the inverse
propor-tionality between the average hrss at Earth and source
distance r: hr ¼ h0r0. Assuming a uniform distribution
in the sky and in time of these standard-candle sources, the expected rate of detections is
Ndet¼ 4RT Z1 0 drr 2ðrÞ ¼ 4RTðh0r0Þ3 Z1 0 dhh 4ðhÞ; (4.3)
whereR is the rate density of the standard-candle sources, T the overall observation time, and ðhÞ the detection efficiency as measured by our simulations.
Hence, the 90% confidence upper limit on rate density R of such standard-candle sources is
R90%¼ 2:3 4Tðh0r0Þ3 R1 0 dhh4ðhÞ : (4.4)
The resultingR90% is dominated by the part of the
detec-tion efficiency curve at small GW amplitude h. Because of
FIG. 5. Upper limits at 90% confidence on the rate of gravitational-wave bursts at Earth as a function of hrss signal
amplitude for selected sine-Gaussian waveforms with Q ¼ 9. The results include all the LIGO and LIGO–Virgo observations since November 2005.
TABLE V. The five most significant events present in the on-source data. IFAR is the inverse false alarm rate [yr] of the event in the entire search, SNR is the signal-to-noise ratio in the whole network, and FAP is the false alarm probability (probability of getting at least as many accidental events as those observed with IFAR the value reported in the first column).
IFAR [yr] Freq. band Network SNR FAP
0.64 0.2–1.6 kHz H1L1 11 0.59
0.36 64–200 Hz H1L1V1 19 0.47
0.28 0.2–1.6 kHz H1L1 12 0.33
0.19 0.2–1.6 kHz H1L1 10 0.35
0.17 1.6–5 kHz H1V1 9 0.24
FIG. 6. Rate limit per unit volume for standard-candle sources at the 90% confidence level for a linearly polarized sine-Gaussian standard-candle with EGW¼ Mc2. Within an
accu-racy of a few percent, the same numerical results hold also for sources emitting circularly polarized GWs, which would sub-sequently appear elliptically polarized at the Earth. In this Figure, all LIGO and LIGO–Virgo observations since November 2005 have been combined together.
the relative orientations of the LIGO-Virgo detectors, de-tection efficiency curves for linearly polarized sine-Gaussian waveforms are approximately the same of those for elliptically polarized ones; the numerical values of R90% are close within a few percent for both source
models.
Figure 6 shows the rate density upper limits of sources as a function of frequency. This result can be interpreted in the following way: given a standard-candle source with a characteristic frequency f and energy EGW, the corresponding rate limit is R90%ðfÞ
ðMc2=EGWÞ3=2 yr1Mpc3.
The typical GW energy in units of solar masses for LIGO-Virgo observation is shown in Fig. 7 computed with Eq. (4.2) using the measured hrss at 50% detection
efficiency for the tested waveforms assuming a standard-candle source emitting at a distance of 10 kpc. The mass scales with the square of the fiducial distance and the results are robust over the very wide class of waveforms tested. As expected, the GW energy is strongly dependent on the spectral sensitivity of the network, with a negligible dependence on the specific waveform characteristics.
V. SUMMARY AND DISCUSSION
This paper reports the results achieved by the LIGO and Virgo detectors in the search for GW transients of duration & 1 s, without assumptions on the signal waveform, po-larization, direction or arrival time.
Three detectors were operating at the Hanford, Livingston and Pisa sites during the second joint observa-tion of LIGO and Virgo in 2009–2010. The detectors implemented hardware upgrades in order to prototype new subsystems planned for the upcoming advanced detectors. The resulting sensitivities to GWs were comparable to those achieved during the first LIGO-Virgo run. The main contribution of the second run is a 50% increase in accumulated observation time.
No event candidates were found in this search. We set better upper limits on the rate of gravitational-wave bursts at Earth and on the rate density of burst sources per unit time and volume. These limits combine all available infor-mation from the LIGO–Virgo joint runs and set the state-of-the-art on all-sky searches for transient gravitational waves of short duration.
The reported hrss amplitude of the GW at Earth can be
converted into the energy emitted by a source at some fiducial distance assuming a simple model as in Eq. (4.2). For example, the energy emitted in gravitational waves in units of solar masses at a distance of 10 kpc and consider-ing measured hrss at 50% detection efficiency (Table II)
is ’ 2:2 108M for signal frequencies near 150 Hz
(5:6 102M at 16 Mpc). These GW energies, though
obviously depending on the signal frequency, are approxi-mately constant over different polarization models of the GW emission, including linearly polarized sources, circu-larly polarized sources and unpolarized emission with random polarization amplitudes (see TablesII,III, andIV). The long baseline interferometric detectors LIGO and Virgo are currently being upgraded to their advanced con-figurations, and the next joint observation is planned for 2015. Another advanced detector, LCGT [37,38], is being built in Japan, and there are proposals to realize an addi-tional advanced LIGO detector outside the USA. These advanced detectors should achieve strain sensitivities a factor of 10 better than the first-generation detectors. For example, at design sensitivity these detectors should detect a typical core-collapse supernova anywhere in the galaxy [39] and will be able to put constraints on extreme scenar-ios for core-collapse supernovae within the local group [4,40]. Other possible short duration sources, such as the merger of very high mass stellar black hole binaries, could be visible at distances exceeding 1 Gpc. During advanced detector observations, gravitational-wave detections are predicted to occur on a regular basis [41], thus greatly expanding the field of gravitational-wave astrophysics.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the support of the United States National Science Foundation for the con-struction and operation of the LIGO Laboratory, the Science and Technology Facilities Council of the United Kingdom, the Max-Planck-Society and the State of Niedersachsen/Germany for support of the construction and operation of the GEO 600 detector, and the Italian Istituto Nazionale di Fisica Nucleare and the French Centre National de la Recherche Scientifique for the construction and operation of the Virgo detector. The authors also grate-fully acknowledge the support of the research by these agencies and by the Australian Research Council, the Council of Scientific and Industrial Research of India, the Istituto Nazionale di Fisica Nucleare of Italy, the Spanish Ministerio de Educacio´n y Ciencia, the Conselleria
FIG. 7. Typical GW energy in solar masses at 50% detection efficiency for standard-candle sources emitting at 10 kpc for the waveforms listed in Tables II, III, and IV considering the H1L1V1 network and the LIGO-Virgo observations since July 2009.
d’Economia Hisenda i Innovacio´ of the Govern de les Illes Balears, the Foundation for Fundamental Research on Matter supported by the Netherlands Organisation for Scientific Research, the Polish Ministry of Science and Higher Education, the FOCUS Programme of Foundation for Polish Science, the Royal Society, the Scottish Funding Council, the Scottish Universities Physics Alliance, the National Aeronautics and Space Administration, the Carnegie Trust, the Leverhulme Trust, the David and Lucile Packard Foundation, the Research Corporation, and the Alfred P. Sloan Foundation. This document
has been assigned LIGO Laboratory document
number LIGO-P1100118-v16.
APPENDIX A: DATA QUALITY FLAGS DQFs are intended to indicate periods of data taking which suffer from environmental and instrumental effects inducing noise into the data [29]. We followed the DQF strategy used in previous searches [16–18], organizing DQFs into 3 categories. The different categories reflect the level of understanding of the detectors’ performances as well as of the relation between disturbances in the data set and environmental or instrumental causes.
Category 1 DQFs mark segments of time (typically more than tens of seconds) when disturbances make analysis unfeasible. Data segments remaining after their application are used in the analysis.
Category 2 DQFs are connected to well-understood short duration (typically a few seconds) periods of noise transients. Data segments flagged by this category can be used for data conditioning and noise property estimation, but events emerging from these periods are discarded as very likely originating from the detector environment.
Finally, Category 3 DQFs denote periods that are only weakly correlated to environmental and instrumental moni-tors. Such cuts are not reliable enough to be used as uncon-ditional cuts. When applied to events generated by the search algorithm, they would reject a significant fraction (in extreme cases up to 15–20%) of data. Their use is limited to significance calculations using the modified in-verse false alarm rate (MIFAR) statistic (see AppendixD).
APPENDIX B: EVENT-BY-EVENT VETOES Often, GW candidate events identified in the on-source time can be linked to disturbances propagating through the detector from the environment or within the detector itself. Our procedure for identifying such event-by-event vetoes in S6 and VSR2/3 follows that used in S5 and VSR1 [16,18]. The GW channel and a large number of auxiliary channels are processed with the Kleine-Welle [42] algo-rithm, which looks for excess power transients. A hierarch-ical method [43] is used to rank the statistical relationship between the transients found in the auxiliary channels and those found in the detector output. Based on these
rank-ings, vetoes are defined for suspected noise events. Another veto used was based on significant statistical association of events observed in the GW channel and the auxiliary channels [44].
An additional set of Category 3 vetoes [45] are applied to events emerging from networks including Virgo; vetoes from this set are based on detector readout channels which are known to be insensitive to gravitational waves.
Procedurally, the event-by-event vetoes are applied with the same conditions as their corresponding category of data quality flags described in AppendixA.
APPENDIX C: DETECTOR NETWORKS AND LIVE TIMES
The total observation time for the analysis has been divided into four subperiods (labeled A, B, C and D), separated by planned commissioning and upgrade breaks which changed the performance of the detectors. TableVI shows the observation time of each network configuration after the application of Category 1 and 2 DQFs. These times are not overlapping. During the period from January to June 2010 (subperiod C), Virgo did not participate in the run because of hardware upgrades.
APPENDIX D: MODIFIED INVERSE FALSE ALARM RATE
We introduce the MIFAR to account for the effect of Category 3 DQFs on the background.
Category 3 DQFs indicate a weak statistical correlation of the GW data with environmental and instrumental noise sources, and thus were used only as a cautionary tag when examining an event in candidate follow-ups. Moreover, the effectiveness of these flags is not constant between differ-ent subperiods, network configurations or frequency bands. The use of Category 3 data quality as a tag allows us to produce two sets of events: the ‘‘raw’’ set (polluted to some extent by noise glitches) and the subset of those events that are not tagged, the ‘‘clean’’ set (with reduced observation time).
TABLE VI. Observation time for each detector configuration after application of Category 1 and 2 DQFs for the four sub-periods A, B, C, and D. For period A, the observation time of the H1L1 network after subtracting the H1L1V1 observation time is negligible ( 1 day). During period C, Virgo did not participate in the run.
detectors A [days] B [days] C [days] D [days] TOT [days]
H1L1V1 10.6 16.7 - 24.9 52.2
H1L1 - 6.2 51.4 26.8 84.5
L1V1 10.2 10.7 - 8.1 28.9
H1V1 12.6 21.3 - 7.1 41.0
In order to account for the difference in background distributions when assessing the significance of candidate GW events from the raw and clean sets, we use the follow-ing procedure:
(1) Within each homogeneous analysis (same detector’s configuration, same tuning of analysis, same fre-quency band), we rank events from the two sets separately by their coherent network amplitude ; i.e., if the event candidate is flagged by Category 3 data quality, it is ranked against the raw set of events, otherwise it is ranked against the clean set. (2) Each event is then assigned a MIFAR as the inverse
of the rate of higher-ranked background events in that set, i.e. the MIFAR is the IFAR of the event considering only that set.
(3) We merge the events from the raw and clean sets into a single list, sorted by the MIFAR. For events with equal MIFAR the one with larger is ranked higher. This ranking is performed separately for each homogeneous analysis.
(4) According to this merged ranking, we measure the IFAR of the events as the rate of the corresponding background event with equal MIFAR. This mea-sured IFAR is used as our ‘‘universal’’ ranking for all events in all analyses.
(5) The final IFAR of any event over the entire search is just 1=3 of the value estimated in the previous step because of the trials factor: three independent analy-ses have been performed for the three disjoint fre-quency bands. No contribution to the trials factor comes from the analyses of different detectors’ con-figuration since these were performed on nonover-lapped observation times.
In each homogeneous analysis, setting a threshold on IFAR corresponds to two thresholds on , one for the raw set and one for the clean data set. Table VIIreports the selected thresholds. These thresholds were tuned using the background and injection events, without con-sidering the on-source events to avoid bias in candidate selection.
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![TABLE V. The five most significant events present in the on- on-source data. IFAR is the inverse false alarm rate [yr] of the event in the entire search, SNR is the signal-to-noise ratio in the whole network, and FAP is the false alarm probability (probabi](https://thumb-eu.123doks.com/thumbv2/123doknet/13930110.450604/12.918.82.442.758.979/table-significant-events-present-inverse-network-probability-probabi.webp)
